Homotopy Lifting Property
If we have a homotopy H : X × → Y and a cover p : Y → Y and we are given a map h0 : X → Y such that H0 = p ○ h0 (h0 is called a lift of h0), then we can lift all H to a map H : X × → Y such that p ○ H = H. The homotopy lifting property is used to characterize fibrations.
Read more about this topic: Homotopy
Famous quotes containing the words lifting and/or property:
“Strange that so few ever come to the woods to see how the pine lives and grows and spires, lifting its evergreen arms to the light,—to see its perfect success; but most are content to behold it in the shape of many broad boards brought to market, and deem that its true success! But the pine is no more lumber than man is, and to be made into boards and houses is no more its true and highest use than the truest use of a man is to be cut down and made into manure.”
—Henry David Thoreau (1817–1862)
“We do not deride the fears of prospering white America. A nation of violence and private property has every reason to dread the violated and the deprived.”
—June Jordan (b. 1939)